Benchmark Calculations of Energetic Properties of Groups 4 and 6 Transition Metal Oxide Nanoclusters Including Comparison to Density Functional Theory

Electronic Structure of Diatomic Nickel Sulfide

The nature of the Ni-S bond is investigated due to its role in the absorption of atmospheric Lewis acid gases such as SO2 and SO3 onto Ni surfaces. The vibrational frequency and electronic structure of NiS were predicted using CCSD(T), CASSCF, and internally contracted multireference configuration interaction (icMRCI) + Q. 43 density functional theory (DFT) functionals were benchmarked. CASSCF predicted the ground state of NiS to be the 5Δ state arising from the 3d8(3F)4s2 (3F) and 3d9(2D)4s (3D) electronic configurations of Ni. When dynamical correlation effects are included at the icMRCI + Q level, the ground state of Ni-S is predicted to be 3Σ- consistent with the experiment. The vibrational frequency of Ni-S is calculated to be 519.1 cm-1 at the icMRCI + Q level, in reasonable agreement with the experimental value of 512.68 cm-1. CCSD(T) predicts the frequency of Ni-S to be 543.2 cm-1 when extrapolated to the complete basis set (CBS) limit. The Feller-Peterson-Dixon value based on the CCSD(T)/CBS extrapolation for the bond dissociation energy of NiS is 350.6 kJ/mol, within <4 kJ/mol of experiment. Of the 43 DFT functionals, BP86 and O3LYP predicted the vibrational frequency in closest agreement with the experiment. The applicability of DFT to such acid gas systems was further demonstrated by calculating the energy for displacement of NiO by SO to yield NiS and O2. This displacement energy was calculated to be within experimental error for ∼50% of the DFT functionals, but large differences were also predicted for some functionals.

The electronic structure of diatomic nickel oxide

The nature of the Ni-O bond is relevant to catalytic and environmental applications. The vibrational frequency and electronic structure of NiO were calculated using CASSCF, icMRCI+Q, CCSD(T), and DFT. CASSCF predicted a quintet state (5Σ-) ground state for the equilibrium bond distance with a state crossing at 1.65 Å, where the triplet (3Σ-) state becomes of lower energy. These states arise from the 3d8(3F)4s2 (3F) and 3d9(2D)4s1 (3D) configurations of Ni. The icMRCI+Q method predicts a triplet (3Σ-) ground state and does not predict a state crossing with the quintet. This state has significant ionic character with the 2pz of O bonding with the 4s/3dz2 of the Ni to form a σ bond. The NiO frequency at the icMRCI+Q level of 835.0 cm-1 is in excellent agreement with experiment; the value of re is 1.5992 Å at this computational level. CCSD(T) predicts ωe = 888.80 cm-1 when extrapolated to the complete basis set limit. Frequencies predicted using CCSD(T) deviate from experiment consistent with the calculations showing large multireference character. A wide array of density functionals were benchmarked. Of the 43 functionals tested, the ones that gave the best prediction of the frequency are ωB97XD, CAM-B3LYP, and τ-HCTH with respective values of 831.8, 838.3, and 837.4 cm-1 respectively. The bond dissociation energy (BDE) of NiO is predicted to be 352.4 kJ mol-1 at the Feller-Peterson-Dixon (FPD) level in good agreement with one of the experimental values. The calculated BDEs at the DFT level are sensitive to the choice of functional and atomic asymptote. Sixteen functionals predicted the BDE within 20 kJ mol-1 of the FPD value.

Binding of SO3 to Group 4 Transition Metal Oxide Nanoclusters

Transition metal oxide (TMO) clusters are being studied for their ability to absorb acid gases generated by energy production processes. The interaction of SO3, a byproduct of common industrial processes, with group 4 metal (Ti, Zr, and Hf) oxide nanoclusters, has been predicted using electronic structure methods. The calculations were done at the density functional theory (DFT) and correlated molecular orbital coupled cluster singles and doubles CCSD(T) theory levels. There is a reasonable agreement between the DFT/ωB97x-D energies with the CCSD(T) results. SO3 is predicted to strongly chemisorb to these clusters, as do NO2 and CO2. For SO3, these chemisorption processes favor binding to TMO clusters as SO42- sulfate in both the terminal and bridging configurations. It is predicted that SO3 fully extracts the bridging oxygen from the TMO lattice to form bridging SO42-. This is favorable because of the lower S-O bond dissociation energy of SO3, whereas other acid gases add across the bridging oxygen because of their higher A-O bond dissociation energy. SO3 is capable of physisorption as long as an exposed metal center is present in the lattice. If a metal center has a terminal oxo-group, then SO3 will prefer the SO42- configuration. An approximately linear relationship exists between the physisorption energy and proton affinity for rows 2 and 3 elements.

Prediction of the structures and heats of formation of MO2, MO3, and M2O5 for M = V, Nb, Ta, Pa

Structures for the mono-, di-, and tri-bridge isomers of M₂O₅ as well as those for the MO₂ and MO₃ fragments for M = V, Nb, Ta, and Pa were optimized at the density functional theory (DFT) level. Single point CCSD(T) calculations extrapolated to the complete basis set (CBS) limit at the DFT geometries were used to predict the energetics. The lowest energy dimer isomer was the di-bridge for M = V and Nb and the tri-bridge for M = Ta and Pa. The di-bridge isomers were predicted to be composed of MO₂⁺ and MO₃^- fragments, whereas the mono- and tri-bridge are two MO₂⁺ fragments linked by an O^2-. The heats of formation of M₂O₅ dimers, as well as MO₂ and MO₃ neutral and ionic species were predicted using the Feller-Peterson-Dixon (FPD) approach. The heats of formation of the MF₅ species were calculated to provide additional benchmarks. Dimerization energies to form the M₂O₅ dimers are predicted to become more negative going down group 5 and range from -29 to -45 kcal mol^-1. The ionization energies (IEs) for VO₂ and TaO₂ are essentially the same at 8.75 eV whereas the IEs for NbO₂ and PaO₂ are 8.10 and 6.25 eV, respectively. The predicted adiabatic electron affinities (AEAs) range from 3.75 eV to 4.45 eV for the MO₃ species and vertical detachment energies from 4.21 to 4.59 eV for MO₃^-. The calculated MO bond dissociation energies increase from 143 kcal mol^-1 for M = V to ∼170 kcal mol^-1 for M = Nb and Ta to ∼200 kcal mol^-1 for M = Pa. The M-O bond dissociation energies are all similar ranging from 97 to 107 kcal mol^-1. Natural bond analysis provided insights into the types of chemical bonds in terms of their ionic character. Pa₂O₅ is predicted to behave like an actinyl species dominated by the interactions of approximately linear PaO₂⁺ groups.

Performance of Density Functionals and Semiempirical 3c Methods for Small Gold-Thiolate Clusters

In light of the recent surge in computational studies of gold thiolate clusters, we present a comparison of popular density functionals (DFAs) and three-part corrected methods (3c-methods) on their performance by taking a data set named as AuSR18 consisting of 18 isomers of Au_n(SCH₃)_m (m ≤ n = 1-3). We have compared the efficiency and accuracy of the DFAs and 3c-methods in geometry optimization with RI-SCS-MP2 as the reference method. Similarly, the performance for accurate and efficient energy evaluation was compared with DLPNO-CCSD(T) as the reference method. The lowest energy structure among the isomers of the largest stoichiometry from our data set, AuSR18, i.e., Au₃(SCH₃)₃, is considered to evaluate the computational time for SCF and gradient evaluations. Alongside this, the numbers of optimization steps to locate the most stable minima of Au₃(SCH₃)₃ are compared to assess the efficiency of the methods. A comparison of relevant bond lengths with the reference geometries was made to estimate the accuracy in geometry optimization. Some methods, such as LC-BLYP, ωB97M-D3BJ, M06-2X, and PBEh-3c, could not locate many of the minima found by most of the other methods; thus, the versatility in locating various minima is also an important criterion in choosing a method for the given project. To determine the accuracy of the methods, we compared the relative energies of the isomers in each stoichiometry and the interaction energy of the gold core with the ligands. The dependence of basis set size and relativistic effects on energies are also compared. The following are some of the highlights. TPSS has shown accuracy, while mPWPW shows comparable speed and accuracy. For the relative energies of the clusters, the hybrid range-separated DFAs are the best option. CAM-B3LYP excels, whereas B3LYP performs poorly. Overall, LC-BLYP is a balanced performer considering both the geometry and relative stability of the structures, but it lacks diversity. The 3c-methods, although fast, are less impressive in relative stability.

Oxygen Deficiencies in Titanium Oxide Clusters as Models for Bulk Defects

TD-DFT calculations were performed on neutral Ti_nO_2n, Ti_nO_2n-1, and Ti_nO_2n-2 clusters, where n ≤ 7. Calculations show the Ti_nO_2n clusters are closed shell systems containing empty d orbitals and that the partially filled d orbitals of the suboxide clusters have a profound effect on their structural, electronic, and topological properties. The low energy photoexcitations of Ti_nO_2n clusters are all O-2p to Ti-3d transitions, while the open-shell suboxide clusters are all characterized by d-d transitions that occur at a much smaller optical gap. Upon low energy photoabsorption, the localization of the hole is accompanied by a local bond elongation, i.e., polaron formation, whereas d-electrons are generally delocalized around the cluster. The properties of the clusters, including the oxygen binding energies and structures, were calculated to account for the variation in relative populations found in experimental cluster distributions. Several Ti_nO_2n-2 clusters contain higher symmetry which is reflected in their relative stability. In particular, the tetrahedral symmetry of Ti₄O₆ inhibits charge carrier localization and therefore exhibits higher stability.

Tuning metathesis performance of molybdenum oxide-based catalyst by silica support acidity modulation and high temperature pretreatment

Molybdenum oxide-based catalysts containing 5 wt. % of Mo obtained by simple impregnation of silica mesoporous support were studied in olefin metathesis reaction at 50 °C. Effect of support modification...

Binding and stability of MgO monomers on anatase TiO2(101)

In catalysis, MgO is often used to modify the acid-base properties of support oxides and to stabilize supported metal atoms and particles on oxides. In this study, we show how the sublimation of MgO powder can be used to deposit MgO monomers, hither on anatase TiO₂(101). A combination of x-ray electron spectroscopy, high-resolution scanning tunneling microscopy, and density functional theory is employed to gain insight into the MgO monomer binding, electronic and vibrational properties, and thermal stability. In the most stable configuration, the Mg and O of the MgO monomer bind to two surface oxygens and one undercoordinated surface titanium, respectively. The additional binding weakens the Mg-O monomer bond and makes Mg more ionic. The monomers are thermally stable up to 600 K, where the onset of diffusion into the TiO₂ bulk is observed. The monomeric MgO species on TiO₂(101) represent an ideal atomically precise system with modified acid-base properties and will be employed in our future catalytic studies.

Reaction of NO2 with Groups IV and VI Transition Metal Oxide Clusters

The addition of NO₂ to Group IV (MO₂)_n and Group VI (MO₃)_n (n = 1-3) nanoclusters was studied using both density functional theory (DFT) and coupled cluster theory (CCSD(T)). The structures and overall binding energetics were predicted for Lewis acid-base addition without transfer of spin (a physisorption-type process) and the formation of either cluster-ONO (HONO-like or bidentate bonding) or NO₃^- formation where for both the spin is transferred to the metal oxide clusters (a chemisorption-type process). Only chemisorption of NO₂ is predicted to be thermodynamically allowed at temperatures ≥298 K for Group IV (MO₂)_n clusters with the formation of surface chemisorbed NO₂ being by far the most energetically favorable. The ligand binding energies (LBEs) for physisorption and chemisorption on the TiO₂ nanoclusters are consistent with computational studies of the bulk solids. Chemisorption is only predicted to occur for (CrO₃)_n clusters in the form of a terminal nitrate containing species whereas the larger chemisorbed nitrate structures for (MoO₃)_n and (WO₃)_n were found to be metastable and unlikely to form in any appreciable amount at temperatures of 298 K and higher. NO₂ is predicted to only be capable of physisorbing to (MoO₃)_n and (WO₃)_n at lower temperatures and therefore unlikely to bind NO₂ at temperatures ≥298 K. Correlations between the (MO₃)_nNO₂ ligand bond energies and the chemical properties of the parent (MO₃)_n clusters (Lewis acidity, ionization potentials, excitation energies, and M = O/M-O bond strengths) are described.

Hydrogenation of 3d-metal oxide clusters: Effects on the structure and magnetic properties

The geometrical structures and properties of the M₈ O₁₂ , M₈ O₁₂ H₈ , and M₈ O₁₂ H₁₂ clusters are explored using density functional theory with the generalized gradient approximation for all 3d-metals M from Sc to Zn. It is found that the geometries and total spin magnetic moments of the clusters depended strongly on the 3d-atom type and the hydrogenation extent. More than the half of all of the 30 clusters had singlet lowest total energy states, which could be described as either nonmagnetic or antiferromagnetic. Hydrogenation increases the total spin magnetic moments of the M₈ O₁₂ H₁₂ clusters when MMnNi, which become larger by four Bohr magneton than those of the corresponding unary clusters M₈ . Hydrogenation substantially affects such properties as polarizability, forbidden band gaps, and dipole moments. Collective superexchange where the local total spin magnetic moments of two atom squads are coupled antiparallel was observed in antiferromagnetic singlet states of Fe₈ O₁₂ H₈ and Co₈ O₁₂ H₈ , whereas the lowest total energy states of their neighbors Mn₈ O₁₂ H₈ and Ni₈ O₁₂ H₈ are ferrimagnetic and ferromagnetic, respectively. Hydrogenation leads to a decrease in the average binding energy per atom when moving across the 3d-metal atom series. © 2018 Wiley Periodicals, Inc.

Modeling σ-Bond Activations by Nickel(0) Beyond Common Approximations: How Accurately Can We Describe Closed-Shell Oxidative Addition Reactions Mediated by Low-Valent Late 3d Transition Metal?

Accurate modelings of reactions involving 3d transition metals (TMs) are very challenging to both ab initio and DFT approaches. To gain more knowledge in this field, we herein explored typical σ-bond activations of H-H, C-H, C-Cl, and C-C bonds promoted by nickel(0), a low-valent late 3d TM. For the key parameters of activation energy (ΔE^‡) and reaction energy (ΔE_R) for these reactions, various issues related to the computational accuracy were systematically investigated. From the scrutiny of convergence issue with one-electron basis set, augmented (A) basis functions are found to be important, and the CCSD(T)/CBS level with complete basis set (CBS) limit extrapolation based on augmented double-ζ and triple-ζ basis pair (ADZ and ATZ), which produces deviations below 1 kcal/mol from the reference, is recommended for larger systems. As an alternative, the explicitly correlated F12 method can accelerate the basis set convergence further, especially after its CBS extrapolations. Thus, the CCSD(T)-F12/CBS(ADZ-ATZ) level with computational cost comparable to the conventional CCSD(T)/CBS(ADZ-ATZ) level, is found to reach the accuracy of the conventional CCSD(T)/A5Z level, which produces deviations below 0.5 kcal/mol from the reference, and is also highly recommendable. Scalar relativistic effects and 3s3p core-valence correlation are non-negligible for achieving chemical accuracy of around 1 kcal/mol. From the scrutiny of convergence issue with the N-electron basis set, in comparison with the reference CCSDTQ result, CCSD(T) is found to be able to calculate ΔE^‡ quite accurately, which is not true for the ΔE_R calculations. Using highest-level CCSD(T) results of ΔE^‡ in this work as references, we tested 18 DFT methods and found that PBE0 and CAM-B3LYP are among the three best performing functionals, irrespective of DFT empirical dispersion correction. With empirical dispersion correction included, ωB97XD is also recommendable due to its improved performance.

Prediction of Bond Dissociation Energies/Heats of Formation for Diatomic Transition Metal Compounds: CCSD(T) Works

It was recently reported ( J. Chem. Theory Comput. 2015 , 11 , 2036 - 2052 ) that the coupled cluster singles and doubles with perturbative triples method, CCSD(T), should not be used as a benchmark tool for the prediction of dissociation energies (heats of formation) for the first row transition metal diatomics based on a comparison with the experimental thermodynamic values for a set of 20 diatomics. In the present work the bond dissociation energies as well as the heats of formation for those diatomics have been calculated by the Feller-Peterson-Dixon approach at the CCSD(T)/complete basis set (CBS) level of theory including scalar relativistic corrections and correlation of the outer shell of core electrons in addition to the valence electrons. Revised experimental values for the hydrides are presented that are based on new heterolytic R-H bond dissociation energies, which are needed for analysis of the mass spectrometry experiments. The agreement between the calculated bond dissociation energies and the revised experimental values of the hydrides is good. Good agreement of the calculated bond dissociation energies/heats of formation is also found for most of the chlorides, oxides, and sulfides given the experimental error bars from experiment and those of the transition metal atoms in the gas phase. Thus, reliable results can be achieved by the CCSD(T) method at the CBS limit. The use of PW91 orbitals for the CCSD(T) calculations improves the predictions for some compounds with large T₁ diagnostics at the HF-CCSD(T) level. The optimized bond distances and calculated vibrational frequencies for the diatomics also agree well with the available experimental values.